Previous studies which examined the relationship between working memory (WM) ability and children's mathematics performance typically measured mathematics ability as a general skill (e.g. Gathercole & Pickering, 2000a) or mental arithmetic ability (e.g. Adams & Hitch, 1997), used number- or digit-based WM assessments and did not control for individual differences in a child's general ability (e.g. intelligence). The aim of this thesis was to extend this research to investigate the associations between the components of the tripartite WM model (e.g. Baddeley, 1986) and a range of mathematical skills in 7-/8- and 9-/10-year-olds using non-digit- based WM assessments, controlling for a measure of general ability. The relationship between WM ability and children's curriculum-based mathematics performance was investigated using a correlational design in Chapters 3 and 4. Assessments, developed in Chapter 2, were used to measure four mathematical skills outlined in the National Curriculum for England. The results indicated that central executive and visuo-spatial sketchpad, but not phonological loop, scores predicted unique variance in performance across all four mathematical skills, even when controlling for NVIQ. Furthermore, both WM abilities were found to predict Key Stage 2 mathematics achievement one year after initial testing (Chapter 8).The same methodology was used in Chapters 6 and 7 to explore the relationship between WM ability and children's performance-related mathematics abilities (see chapter 5). All three components of WM predicted unique variance in these mathematical skills, but a markedly distinct pattern of associations was revealed between the two age groups. In particular, the data implicated a stronger role for the visuo-spatial sketchpad in the younger children's mathematics. The role of visuo-spatial WM in children's mathematics was explored further in Chapter 9 where a discrepancy definition was applied to identify children with poor mathematics or poor visuo-spatial abilities. The data provided an initial indication that normal visuo-spatial sketchpad development may be important for normal mathematics development. The overarching conclusion is that WM, and the central executive and visuo- spatial sketchpad in particular, may support the development of early mathematical ability. The practical and theoretical implications of these findings are considered.